Key lawmakers see opportunity this session to address immigration reform but remain stymied on a central issue: whether to tackle it in chunks or in one complete package.

“Every member of Congress will find something in a comprehensive bill that they will not like,” Rep. Raul Labrador (R-Idaho) said at Tuesday’s POLITICO Pro Tech Deep Dive focused on Immigration, Technology and the 113th Congress. “We should have a series of bills — four, five or six bills — that we debate separately but that we vote together on the House floor.”

Labrador accused the White House of aiming for a “political victory” instead of a “policy victory.”

Silicon Valley Democrat Zoe Lofgren redirected the blame to Congress. “I have had Republicans say they don’t want Obama to do a bill because they want flexibility, but if he doesn’t do a bill, he’s criticized,” she said. “I’m waiting for a signal from the speaker on what he wants to do. It’s not that tough, it’s just the decision to do it.”

Tech companies are lobbying hard for immigration reforms that would allow foreign employees to fill unmet demand and ensure they maintain global competitiveness. And all three lawmakers agree the system needs fixing. The difficulty lies in figuring out how to do it.

But the issue is a special challenge for Republicans, who must reconcile shifting demographics and a history of no-mercy enforcement.

Chaffetz pushed a bill last session that would have lifted the country caps on visas for high-skilled workers. Tech companies like Microsoft and Google embraced the bill. The legislation passed the House but failed in the Senate.

And Labrador has become a leading GOP voice on immigration changes, saying his decision to run for governor hinges on whether Congress implements reforms. He and Chaffetz advocated last session for legislation that would have granted up to 55,000 visas to noncitizens who complete certain science, technology, engineering and math degrees at American universities. Democrats lambasted the bill, known as the STEM Jobs Act, as a token Republican move to garner minority support. The Senate shot the bill down.

“I want us to be known as the pro-immigration party,” Labrador said. “I want us to be known that we welcome people to this country, that we want people to be successful. I want our party to take this lead on immigration reform.”

Democrats in both chambers are pushing for more overarching legislation, calling smaller attempts political posturing.

“Everybody wants their piece,” Lofgren said. “You talk to the ag people, you can’t do the tech thing because we need migrant farm workers. You’ve got husbands and wives separated for half a decade. What’s that do for our country? We have 2 million migrant farm workers who don’t have their papers, and without them we don’t have an agricultural industry.”

Lofgren has advocated for encompassing legislation that would grant citizenship to some undocumented immigrants who came to the United States at an early age and go on to college or the military.

“I know these guys want to get something done,” she said. “The Republicans are going to lose, lose, lose if they don’t change on this issue. But it’s not the same political calculation within districts.”

President Barack Obama has vowed to prioritize the issue this session, likely in one comprehensive bill. This would avoid Republican attempts to break it into smaller bits and address highly skilled workers, younger illegal immigrant and farm workers in separate bills.

Immigration groups have voiced angst that the president has not moved faster to enact substantial reform. The administration has deported record numbers of illegal immigrants. But it also has started to make significant strides to expedite changes — even without Congress.

Obama signed an executive order in June that ordered Homeland Security officials to halt deportation proceedings against immigrants who entered the country as children and who have finished high school or joined the military.

Similar legislation known as the DREAM Act has stalled in Congress.

Obama is expected to lay out his plans as soon as his State of the Union speech next month. A bipartisan group of senators also is working on a reform bill.